Simplify the following expression: $ a = \dfrac{-5}{3} - \dfrac{k - 3}{-4k} $
Solution: In order to subtract expressions, they must have a common denominator. Multiply the first expression by $\dfrac{-4k}{-4k}$ $ \dfrac{-5}{3} \times \dfrac{-4k}{-4k} = \dfrac{20k}{-12k} $ Multiply the second expression by $\dfrac{3}{3}$ $ \dfrac{k - 3}{-4k} \times \dfrac{3}{3} = \dfrac{3k - 9}{-12k} $ Therefore $ a = \dfrac{20k}{-12k} - \dfrac{3k - 9}{-12k} $ Now the expressions have the same denominator we can simply subtract the numerators: $a = \dfrac{20k - (3k - 9) }{-12k} $ Distribute the negative sign: $a = \dfrac{20k - 3k + 9}{-12k}$ $a = \dfrac{17k + 9}{-12k}$ Simplify the expression by dividing the numerator and denominator by -1: $a = \dfrac{-17k - 9}{12k}$